I am wondering the number of possible (and logical) combinations for an NFL post-season survivor pool.

The rules of the survivor pool are simple: you have to pick one winner for each round of the playoffs (i.e. 1 of 4 possible wildcard winners, 1 of 4 possible division winners, 1 of 2 possible conference winners, and the superbowl winner), and you can't pick the same team to win in more than one round. The format of the playoffs is available here: NFL Schedule: Playoffs

You have to take into account the fact that once you have picked a winner in an early game, you can't pick the team that lost to your winner to win in a later round, since they've been eliminated (hence the 'logical' reference above)

Can you explain this a bit better to someone who doesn't watch NFL? When you say "Pick a winner" it sounds like they don't have to try to win because you just pick a winner at random like a lottery.
How many teams are there? Do you put teams into pairs or into pools larger than 2? How many pairs or pools do you have to make?